In football, the offense has four chances to travel 10 yards and thus, get a first down. Those chances have names; the first one as already said is called a first down, the second a second down, the third a third down, and the fourth and last a fourth down. All four together is called the down cycle. Every time the offense fails to achieve a first down, a down is recorded. A team's plays are highly based on which stage of a down cycle the team is at, and how many yards they have to travel to get to a first down.
If the offense fails to travel the 10 yards (gets to a first down) in all tries and gets to the fourth down, it either has to turn the ball over to the other team by punting or attempting a field goal. In some cases, teams choose to use the fourth down to try a passing or running play again, but that comes at the risk of giving the opponent a better field position if they don't travel the needed distance in that fourth and last chance.